Documentary theatre is still very much in the ascendant, with recent shows such as Stockwell, The Power of Yes, Katrine and The Girlfriend Experience all drawing on verbatim techniques. But at the Dublin theatre festival over the weekend, I saw Radio Muezzin, an astonishingly effective show from Stefan Kaegi and Rimini Protokoll.

As in the work of Manchester-based company Quarantine (which, in shows such as White Trash and Susan and Darren, has produced an extraordinary body of work that allows ordinary people to present themselves on stage as they want to be seen) or the work of the superb Junction 25 theatre, Radio Muezzin puts real people on stage, not actors. In this instance, they are all Egyptian muezzins, the men who daily call Cairo's faithful to prayer.

Because of advances in technology, we are told, the Egyptian authorities are planning to centralise the azan and broadcast it live over the radio. Just 30 specially chosen muezzins will take it in turns to make the call to prayer. What will this mean for the muezzins who are not among the chosen? Could a centralised live broadcast the same as the current situation where several voices join in one swelling call to prayer, creating a soundscape across the city?

Radio Muezzin goes beyond the question of what 'live' means and addresses the question of representation itself. Rimini Protokoll's "experts in daily life" – in this instance, the muezzins who engage with the audience so directly and unaffectedly – are apparently just being themselves. But is it possible to be yourself on stage? Or can you only create a representation of yourself? What is the difference between acting and performing; performing and being? Which parts of myself am I prepared to show on stage?

Not only does Radio Muezzin give you a direct conduit into other people's lives and another culture, this low-key piece also grapples with the very form of theatre itself – in particular, the issues of co-authorship, ownership and exploitation that arise in documentary theatre. The use of actors in most verbatim-style work allows directors to shape the material in a way that suits their dramatic purpose. But in the case of Radio Muezzin – just as in one of Quarantine's shows – the authors of the piece are present on stage: they present themselves. There is no intermediary.

And yet, are they presenting the truth? Of course they are, although quite possibly only one version of many complex and interweaving truths. One of the interesting things about Radio Muezzin is its recognition that truth is a fabric that's full of holes: at one point we discover that one of the muezzins recently quit the show because of tensions between himself and the other performers. He was one of the chosen 30, the others were not. But was this the reason for his departure, or did being in the show change the people involved and affect their relationships? We will never know.

The strange and rather exhilarating thing about Radio Muezzin is that the more it tells you, the more aware you become of how little you know. It raises more questions than it answers. Foremost among them is this: why it is that this piece of theatre feels far more real than any TV documentary?